Properties

Label 380.2.u.b.101.3
Level $380$
Weight $2$
Character 380.101
Analytic conductor $3.034$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [380,2,Mod(61,380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(380, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("380.61");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.u (of order \(9\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.03431527681\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(3\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - 3 x^{17} + 21 x^{16} - 30 x^{15} + 192 x^{14} - 207 x^{13} + 1178 x^{12} - 705 x^{11} + 4413 x^{10} - 2224 x^{9} + 11430 x^{8} - 4101 x^{7} + 19237 x^{6} - 7125 x^{5} + \cdots + 5329 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 101.3
Root \(1.55777 - 2.69813i\) of defining polynomial
Character \(\chi\) \(=\) 380.101
Dual form 380.2.u.b.301.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.92764 + 1.06558i) q^{3} +(0.173648 + 0.984808i) q^{5} +(0.643760 - 1.11502i) q^{7} +(5.13752 + 4.31089i) q^{9} +O(q^{10})\) \(q+(2.92764 + 1.06558i) q^{3} +(0.173648 + 0.984808i) q^{5} +(0.643760 - 1.11502i) q^{7} +(5.13752 + 4.31089i) q^{9} +(-2.25088 - 3.89864i) q^{11} +(-0.115094 + 0.0418907i) q^{13} +(-0.541007 + 3.06820i) q^{15} +(-0.730551 + 0.613005i) q^{17} +(-1.18925 + 4.19353i) q^{19} +(3.07284 - 2.57842i) q^{21} +(0.507981 - 2.88091i) q^{23} +(-0.939693 + 0.342020i) q^{25} +(5.77395 + 10.0008i) q^{27} +(-5.12896 - 4.30371i) q^{29} +(-2.91189 + 5.04355i) q^{31} +(-2.43548 - 13.8123i) q^{33} +(1.20987 + 0.440358i) q^{35} -8.95982 q^{37} -0.381591 q^{39} +(7.45930 + 2.71496i) q^{41} +(-1.65520 - 9.38710i) q^{43} +(-3.35328 + 5.80804i) q^{45} +(-0.709210 - 0.595097i) q^{47} +(2.67115 + 4.62656i) q^{49} +(-2.79200 + 1.01620i) q^{51} +(-0.00414149 + 0.0234876i) q^{53} +(3.44855 - 2.89368i) q^{55} +(-7.95023 + 11.0099i) q^{57} +(8.19663 - 6.87779i) q^{59} +(1.02491 - 5.81255i) q^{61} +(8.11408 - 2.95328i) q^{63} +(-0.0612401 - 0.106071i) q^{65} +(12.0876 + 10.1427i) q^{67} +(4.55701 - 7.89297i) q^{69} +(-2.62142 - 14.8668i) q^{71} +(3.61254 + 1.31486i) q^{73} -3.11553 q^{75} -5.79610 q^{77} +(-2.80162 - 1.01971i) q^{79} +(2.75375 + 15.6173i) q^{81} +(-4.36455 + 7.55962i) q^{83} +(-0.730551 - 0.613005i) q^{85} +(-10.4299 - 18.0650i) q^{87} +(-14.0616 + 5.11801i) q^{89} +(-0.0273836 + 0.155300i) q^{91} +(-13.8993 + 11.6629i) q^{93} +(-4.33633 - 0.442988i) q^{95} +(-13.3023 + 11.1620i) q^{97} +(5.24266 - 29.7326i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 3 q^{3} + 15 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 3 q^{3} + 15 q^{9} + 9 q^{13} + 3 q^{15} + 12 q^{17} - 18 q^{19} - 9 q^{21} + 21 q^{23} + 18 q^{27} - 9 q^{29} + 6 q^{31} - 21 q^{33} - 6 q^{35} - 36 q^{37} - 12 q^{39} + 6 q^{41} - 12 q^{43} - 6 q^{45} + 21 q^{47} - 3 q^{49} - 9 q^{51} + 36 q^{53} - 3 q^{55} - 24 q^{57} - 6 q^{61} + 36 q^{63} + 15 q^{65} + 60 q^{67} + 27 q^{69} - 36 q^{71} - 60 q^{73} - 6 q^{75} - 36 q^{77} - 3 q^{79} + 3 q^{81} - 6 q^{83} + 12 q^{85} + 21 q^{87} + 6 q^{89} - 30 q^{91} - 48 q^{93} - 21 q^{95} - 57 q^{97} + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.92764 + 1.06558i 1.69028 + 0.615210i 0.994660 0.103204i \(-0.0329093\pi\)
0.695616 + 0.718414i \(0.255132\pi\)
\(4\) 0 0
\(5\) 0.173648 + 0.984808i 0.0776578 + 0.440419i
\(6\) 0 0
\(7\) 0.643760 1.11502i 0.243318 0.421440i −0.718339 0.695693i \(-0.755097\pi\)
0.961657 + 0.274253i \(0.0884307\pi\)
\(8\) 0 0
\(9\) 5.13752 + 4.31089i 1.71251 + 1.43696i
\(10\) 0 0
\(11\) −2.25088 3.89864i −0.678666 1.17548i −0.975383 0.220518i \(-0.929225\pi\)
0.296717 0.954965i \(-0.404108\pi\)
\(12\) 0 0
\(13\) −0.115094 + 0.0418907i −0.0319213 + 0.0116184i −0.357931 0.933748i \(-0.616518\pi\)
0.326010 + 0.945366i \(0.394296\pi\)
\(14\) 0 0
\(15\) −0.541007 + 3.06820i −0.139687 + 0.792206i
\(16\) 0 0
\(17\) −0.730551 + 0.613005i −0.177185 + 0.148676i −0.727067 0.686567i \(-0.759117\pi\)
0.549882 + 0.835242i \(0.314673\pi\)
\(18\) 0 0
\(19\) −1.18925 + 4.19353i −0.272834 + 0.962061i
\(20\) 0 0
\(21\) 3.07284 2.57842i 0.670549 0.562658i
\(22\) 0 0
\(23\) 0.507981 2.88091i 0.105921 0.600710i −0.884927 0.465730i \(-0.845792\pi\)
0.990848 0.134980i \(-0.0430971\pi\)
\(24\) 0 0
\(25\) −0.939693 + 0.342020i −0.187939 + 0.0684040i
\(26\) 0 0
\(27\) 5.77395 + 10.0008i 1.11120 + 1.92465i
\(28\) 0 0
\(29\) −5.12896 4.30371i −0.952425 0.799179i 0.0272796 0.999628i \(-0.491316\pi\)
−0.979704 + 0.200449i \(0.935760\pi\)
\(30\) 0 0
\(31\) −2.91189 + 5.04355i −0.522991 + 0.905847i 0.476651 + 0.879093i \(0.341851\pi\)
−0.999642 + 0.0267547i \(0.991483\pi\)
\(32\) 0 0
\(33\) −2.43548 13.8123i −0.423963 2.40441i
\(34\) 0 0
\(35\) 1.20987 + 0.440358i 0.204506 + 0.0744340i
\(36\) 0 0
\(37\) −8.95982 −1.47299 −0.736493 0.676445i \(-0.763520\pi\)
−0.736493 + 0.676445i \(0.763520\pi\)
\(38\) 0 0
\(39\) −0.381591 −0.0611035
\(40\) 0 0
\(41\) 7.45930 + 2.71496i 1.16495 + 0.424006i 0.850862 0.525389i \(-0.176080\pi\)
0.314085 + 0.949395i \(0.398302\pi\)
\(42\) 0 0
\(43\) −1.65520 9.38710i −0.252415 1.43152i −0.802621 0.596490i \(-0.796562\pi\)
0.550205 0.835030i \(-0.314550\pi\)
\(44\) 0 0
\(45\) −3.35328 + 5.80804i −0.499877 + 0.865812i
\(46\) 0 0
\(47\) −0.709210 0.595097i −0.103449 0.0868039i 0.589596 0.807698i \(-0.299287\pi\)
−0.693045 + 0.720894i \(0.743731\pi\)
\(48\) 0 0
\(49\) 2.67115 + 4.62656i 0.381592 + 0.660937i
\(50\) 0 0
\(51\) −2.79200 + 1.01620i −0.390958 + 0.142297i
\(52\) 0 0
\(53\) −0.00414149 + 0.0234876i −0.000568878 + 0.00322627i −0.985091 0.172035i \(-0.944966\pi\)
0.984522 + 0.175261i \(0.0560770\pi\)
\(54\) 0 0
\(55\) 3.44855 2.89368i 0.465002 0.390183i
\(56\) 0 0
\(57\) −7.95023 + 11.0099i −1.05303 + 1.45830i
\(58\) 0 0
\(59\) 8.19663 6.87779i 1.06711 0.895411i 0.0723223 0.997381i \(-0.476959\pi\)
0.994787 + 0.101970i \(0.0325145\pi\)
\(60\) 0 0
\(61\) 1.02491 5.81255i 0.131226 0.744221i −0.846187 0.532886i \(-0.821108\pi\)
0.977414 0.211335i \(-0.0677813\pi\)
\(62\) 0 0
\(63\) 8.11408 2.95328i 1.02228 0.372079i
\(64\) 0 0
\(65\) −0.0612401 0.106071i −0.00759590 0.0131565i
\(66\) 0 0
\(67\) 12.0876 + 10.1427i 1.47673 + 1.23913i 0.909589 + 0.415509i \(0.136397\pi\)
0.567145 + 0.823618i \(0.308048\pi\)
\(68\) 0 0
\(69\) 4.55701 7.89297i 0.548600 0.950202i
\(70\) 0 0
\(71\) −2.62142 14.8668i −0.311106 1.76437i −0.593271 0.805003i \(-0.702164\pi\)
0.282165 0.959366i \(-0.408947\pi\)
\(72\) 0 0
\(73\) 3.61254 + 1.31486i 0.422816 + 0.153892i 0.544660 0.838657i \(-0.316659\pi\)
−0.121844 + 0.992549i \(0.538881\pi\)
\(74\) 0 0
\(75\) −3.11553 −0.359751
\(76\) 0 0
\(77\) −5.79610 −0.660527
\(78\) 0 0
\(79\) −2.80162 1.01971i −0.315207 0.114726i 0.179572 0.983745i \(-0.442529\pi\)
−0.494779 + 0.869019i \(0.664751\pi\)
\(80\) 0 0
\(81\) 2.75375 + 15.6173i 0.305972 + 1.73525i
\(82\) 0 0
\(83\) −4.36455 + 7.55962i −0.479071 + 0.829776i −0.999712 0.0240000i \(-0.992360\pi\)
0.520641 + 0.853776i \(0.325693\pi\)
\(84\) 0 0
\(85\) −0.730551 0.613005i −0.0792394 0.0664897i
\(86\) 0 0
\(87\) −10.4299 18.0650i −1.11820 1.93677i
\(88\) 0 0
\(89\) −14.0616 + 5.11801i −1.49053 + 0.542508i −0.953588 0.301113i \(-0.902642\pi\)
−0.536939 + 0.843621i \(0.680420\pi\)
\(90\) 0 0
\(91\) −0.0273836 + 0.155300i −0.00287058 + 0.0162799i
\(92\) 0 0
\(93\) −13.8993 + 11.6629i −1.44129 + 1.20938i
\(94\) 0 0
\(95\) −4.33633 0.442988i −0.444898 0.0454496i
\(96\) 0 0
\(97\) −13.3023 + 11.1620i −1.35064 + 1.13332i −0.371891 + 0.928276i \(0.621291\pi\)
−0.978752 + 0.205048i \(0.934265\pi\)
\(98\) 0 0
\(99\) 5.24266 29.7326i 0.526907 2.98824i
\(100\) 0 0
\(101\) 6.82879 2.48548i 0.679490 0.247314i 0.0208616 0.999782i \(-0.493359\pi\)
0.658629 + 0.752468i \(0.271137\pi\)
\(102\) 0 0
\(103\) −0.425234 0.736527i −0.0418996 0.0725722i 0.844315 0.535847i \(-0.180008\pi\)
−0.886215 + 0.463275i \(0.846674\pi\)
\(104\) 0 0
\(105\) 3.07284 + 2.57842i 0.299879 + 0.251628i
\(106\) 0 0
\(107\) 5.04809 8.74355i 0.488017 0.845271i −0.511888 0.859052i \(-0.671054\pi\)
0.999905 + 0.0137816i \(0.00438695\pi\)
\(108\) 0 0
\(109\) −0.521529 2.95774i −0.0499534 0.283300i 0.949591 0.313492i \(-0.101499\pi\)
−0.999544 + 0.0301927i \(0.990388\pi\)
\(110\) 0 0
\(111\) −26.2312 9.54737i −2.48975 0.906196i
\(112\) 0 0
\(113\) −6.06424 −0.570475 −0.285238 0.958457i \(-0.592073\pi\)
−0.285238 + 0.958457i \(0.592073\pi\)
\(114\) 0 0
\(115\) 2.92535 0.272790
\(116\) 0 0
\(117\) −0.771882 0.280942i −0.0713605 0.0259731i
\(118\) 0 0
\(119\) 0.213216 + 1.20921i 0.0195455 + 0.110848i
\(120\) 0 0
\(121\) −4.63292 + 8.02445i −0.421174 + 0.729496i
\(122\) 0 0
\(123\) 18.9452 + 15.8969i 1.70823 + 1.43337i
\(124\) 0 0
\(125\) −0.500000 0.866025i −0.0447214 0.0774597i
\(126\) 0 0
\(127\) −6.24161 + 2.27176i −0.553854 + 0.201586i −0.603758 0.797168i \(-0.706331\pi\)
0.0499042 + 0.998754i \(0.484108\pi\)
\(128\) 0 0
\(129\) 5.15683 29.2458i 0.454033 2.57495i
\(130\) 0 0
\(131\) 7.06862 5.93127i 0.617588 0.518218i −0.279456 0.960158i \(-0.590154\pi\)
0.897044 + 0.441941i \(0.145710\pi\)
\(132\) 0 0
\(133\) 3.91029 + 4.02567i 0.339065 + 0.349070i
\(134\) 0 0
\(135\) −8.84620 + 7.42284i −0.761359 + 0.638856i
\(136\) 0 0
\(137\) −0.634270 + 3.59712i −0.0541893 + 0.307323i −0.999840 0.0178599i \(-0.994315\pi\)
0.945651 + 0.325183i \(0.105426\pi\)
\(138\) 0 0
\(139\) 17.6900 6.43863i 1.50044 0.546117i 0.544269 0.838911i \(-0.316807\pi\)
0.956176 + 0.292794i \(0.0945849\pi\)
\(140\) 0 0
\(141\) −1.44219 2.49795i −0.121454 0.210365i
\(142\) 0 0
\(143\) 0.422379 + 0.354418i 0.0353211 + 0.0296379i
\(144\) 0 0
\(145\) 3.34769 5.79837i 0.278011 0.481529i
\(146\) 0 0
\(147\) 2.89022 + 16.3912i 0.238381 + 1.35193i
\(148\) 0 0
\(149\) −11.0670 4.02805i −0.906641 0.329990i −0.153730 0.988113i \(-0.549129\pi\)
−0.752911 + 0.658122i \(0.771351\pi\)
\(150\) 0 0
\(151\) 6.94029 0.564793 0.282396 0.959298i \(-0.408871\pi\)
0.282396 + 0.959298i \(0.408871\pi\)
\(152\) 0 0
\(153\) −6.39581 −0.517071
\(154\) 0 0
\(155\) −5.47257 1.99185i −0.439567 0.159989i
\(156\) 0 0
\(157\) 3.03157 + 17.1929i 0.241946 + 1.37214i 0.827480 + 0.561495i \(0.189774\pi\)
−0.585534 + 0.810648i \(0.699115\pi\)
\(158\) 0 0
\(159\) −0.0371526 + 0.0643502i −0.00294639 + 0.00510330i
\(160\) 0 0
\(161\) −2.88526 2.42102i −0.227391 0.190803i
\(162\) 0 0
\(163\) 6.12605 + 10.6106i 0.479829 + 0.831089i 0.999732 0.0231364i \(-0.00736520\pi\)
−0.519903 + 0.854225i \(0.674032\pi\)
\(164\) 0 0
\(165\) 13.1796 4.79696i 1.02603 0.373443i
\(166\) 0 0
\(167\) −4.09639 + 23.2318i −0.316988 + 1.79773i 0.243860 + 0.969811i \(0.421586\pi\)
−0.560848 + 0.827919i \(0.689525\pi\)
\(168\) 0 0
\(169\) −9.94709 + 8.34660i −0.765160 + 0.642046i
\(170\) 0 0
\(171\) −24.1876 + 16.4176i −1.84968 + 1.25548i
\(172\) 0 0
\(173\) −7.98365 + 6.69908i −0.606986 + 0.509321i −0.893683 0.448700i \(-0.851887\pi\)
0.286697 + 0.958021i \(0.407443\pi\)
\(174\) 0 0
\(175\) −0.223575 + 1.26796i −0.0169007 + 0.0958487i
\(176\) 0 0
\(177\) 31.3256 11.4016i 2.35458 0.856996i
\(178\) 0 0
\(179\) −4.20212 7.27829i −0.314081 0.544005i 0.665160 0.746701i \(-0.268363\pi\)
−0.979242 + 0.202696i \(0.935030\pi\)
\(180\) 0 0
\(181\) 17.2650 + 14.4870i 1.28329 + 1.07681i 0.992781 + 0.119940i \(0.0382703\pi\)
0.290513 + 0.956871i \(0.406174\pi\)
\(182\) 0 0
\(183\) 9.19428 15.9250i 0.679661 1.17721i
\(184\) 0 0
\(185\) −1.55586 8.82370i −0.114389 0.648732i
\(186\) 0 0
\(187\) 4.03427 + 1.46835i 0.295015 + 0.107377i
\(188\) 0 0
\(189\) 14.8681 1.08150
\(190\) 0 0
\(191\) 24.2967 1.75805 0.879025 0.476775i \(-0.158194\pi\)
0.879025 + 0.476775i \(0.158194\pi\)
\(192\) 0 0
\(193\) 4.36570 + 1.58898i 0.314250 + 0.114378i 0.494330 0.869274i \(-0.335413\pi\)
−0.180080 + 0.983652i \(0.557636\pi\)
\(194\) 0 0
\(195\) −0.0662626 0.375794i −0.00474516 0.0269112i
\(196\) 0 0
\(197\) 6.00361 10.3986i 0.427740 0.740867i −0.568932 0.822384i \(-0.692643\pi\)
0.996672 + 0.0815174i \(0.0259766\pi\)
\(198\) 0 0
\(199\) 8.96006 + 7.51838i 0.635162 + 0.532964i 0.902528 0.430631i \(-0.141709\pi\)
−0.267366 + 0.963595i \(0.586153\pi\)
\(200\) 0 0
\(201\) 24.5804 + 42.5744i 1.73376 + 3.00297i
\(202\) 0 0
\(203\) −8.10057 + 2.94836i −0.568548 + 0.206935i
\(204\) 0 0
\(205\) −1.37842 + 7.81742i −0.0962732 + 0.545993i
\(206\) 0 0
\(207\) 15.0290 12.6108i 1.04459 0.876515i
\(208\) 0 0
\(209\) 19.0259 4.80266i 1.31605 0.332207i
\(210\) 0 0
\(211\) 9.63682 8.08626i 0.663426 0.556681i −0.247685 0.968841i \(-0.579670\pi\)
0.911112 + 0.412160i \(0.135225\pi\)
\(212\) 0 0
\(213\) 8.16713 46.3181i 0.559603 3.17367i
\(214\) 0 0
\(215\) 8.95707 3.26011i 0.610867 0.222337i
\(216\) 0 0
\(217\) 3.74912 + 6.49366i 0.254507 + 0.440819i
\(218\) 0 0
\(219\) 9.17515 + 7.69887i 0.619999 + 0.520241i
\(220\) 0 0
\(221\) 0.0584026 0.101156i 0.00392858 0.00680451i
\(222\) 0 0
\(223\) 2.34163 + 13.2801i 0.156807 + 0.889299i 0.957115 + 0.289709i \(0.0935586\pi\)
−0.800307 + 0.599590i \(0.795330\pi\)
\(224\) 0 0
\(225\) −6.30210 2.29378i −0.420140 0.152918i
\(226\) 0 0
\(227\) −21.1090 −1.40105 −0.700526 0.713627i \(-0.747051\pi\)
−0.700526 + 0.713627i \(0.747051\pi\)
\(228\) 0 0
\(229\) −19.3629 −1.27954 −0.639770 0.768567i \(-0.720970\pi\)
−0.639770 + 0.768567i \(0.720970\pi\)
\(230\) 0 0
\(231\) −16.9689 6.17619i −1.11647 0.406363i
\(232\) 0 0
\(233\) −0.321621 1.82400i −0.0210701 0.119494i 0.972459 0.233075i \(-0.0748789\pi\)
−0.993529 + 0.113581i \(0.963768\pi\)
\(234\) 0 0
\(235\) 0.462904 0.801773i 0.0301965 0.0523019i
\(236\) 0 0
\(237\) −7.11558 5.97068i −0.462207 0.387837i
\(238\) 0 0
\(239\) 10.6784 + 18.4956i 0.690730 + 1.19638i 0.971599 + 0.236633i \(0.0760441\pi\)
−0.280869 + 0.959746i \(0.590623\pi\)
\(240\) 0 0
\(241\) 5.67933 2.06711i 0.365838 0.133154i −0.152559 0.988294i \(-0.548751\pi\)
0.518397 + 0.855140i \(0.326529\pi\)
\(242\) 0 0
\(243\) −2.56358 + 14.5388i −0.164454 + 0.932663i
\(244\) 0 0
\(245\) −4.09243 + 3.43396i −0.261456 + 0.219388i
\(246\) 0 0
\(247\) −0.0387941 0.532467i −0.00246841 0.0338801i
\(248\) 0 0
\(249\) −20.8332 + 17.4811i −1.32025 + 1.10782i
\(250\) 0 0
\(251\) −0.425210 + 2.41149i −0.0268390 + 0.152212i −0.995282 0.0970230i \(-0.969068\pi\)
0.968443 + 0.249235i \(0.0801791\pi\)
\(252\) 0 0
\(253\) −12.3750 + 4.50414i −0.778010 + 0.283173i
\(254\) 0 0
\(255\) −1.48559 2.57312i −0.0930313 0.161135i
\(256\) 0 0
\(257\) 7.75878 + 6.51039i 0.483979 + 0.406107i 0.851863 0.523765i \(-0.175473\pi\)
−0.367884 + 0.929872i \(0.619917\pi\)
\(258\) 0 0
\(259\) −5.76798 + 9.99043i −0.358405 + 0.620775i
\(260\) 0 0
\(261\) −7.79732 44.2208i −0.482642 2.73720i
\(262\) 0 0
\(263\) −10.3651 3.77260i −0.639141 0.232628i 0.00206405 0.999998i \(-0.499343\pi\)
−0.641205 + 0.767370i \(0.721565\pi\)
\(264\) 0 0
\(265\) −0.0238499 −0.00146509
\(266\) 0 0
\(267\) −46.6210 −2.85316
\(268\) 0 0
\(269\) 18.7568 + 6.82690i 1.14362 + 0.416243i 0.843219 0.537570i \(-0.180658\pi\)
0.300400 + 0.953813i \(0.402880\pi\)
\(270\) 0 0
\(271\) −0.988320 5.60504i −0.0600362 0.340482i 0.939964 0.341275i \(-0.110859\pi\)
−1.00000 0.000792933i \(0.999748\pi\)
\(272\) 0 0
\(273\) −0.245653 + 0.425484i −0.0148676 + 0.0257514i
\(274\) 0 0
\(275\) 3.44855 + 2.89368i 0.207955 + 0.174495i
\(276\) 0 0
\(277\) −16.0854 27.8607i −0.966477 1.67399i −0.705594 0.708616i \(-0.749320\pi\)
−0.260883 0.965370i \(-0.584014\pi\)
\(278\) 0 0
\(279\) −36.7021 + 13.3585i −2.19729 + 0.799750i
\(280\) 0 0
\(281\) 2.33744 13.2563i 0.139440 0.790805i −0.832224 0.554440i \(-0.812933\pi\)
0.971664 0.236365i \(-0.0759563\pi\)
\(282\) 0 0
\(283\) 5.76933 4.84104i 0.342951 0.287770i −0.455001 0.890491i \(-0.650361\pi\)
0.797952 + 0.602721i \(0.205917\pi\)
\(284\) 0 0
\(285\) −12.2232 5.91760i −0.724040 0.350528i
\(286\) 0 0
\(287\) 7.82925 6.56952i 0.462146 0.387787i
\(288\) 0 0
\(289\) −2.79409 + 15.8461i −0.164358 + 0.932122i
\(290\) 0 0
\(291\) −50.8383 + 18.5036i −2.98019 + 1.08470i
\(292\) 0 0
\(293\) 12.3915 + 21.4627i 0.723919 + 1.25386i 0.959418 + 0.281989i \(0.0909942\pi\)
−0.235499 + 0.971875i \(0.575672\pi\)
\(294\) 0 0
\(295\) 8.19663 + 6.87779i 0.477226 + 0.400440i
\(296\) 0 0
\(297\) 25.9929 45.0210i 1.50826 2.61239i
\(298\) 0 0
\(299\) 0.0622176 + 0.352854i 0.00359814 + 0.0204061i
\(300\) 0 0
\(301\) −11.5324 4.19745i −0.664717 0.241937i
\(302\) 0 0
\(303\) 22.6407 1.30068
\(304\) 0 0
\(305\) 5.90222 0.337960
\(306\) 0 0
\(307\) 16.1933 + 5.89388i 0.924200 + 0.336381i 0.759908 0.650031i \(-0.225244\pi\)
0.164292 + 0.986412i \(0.447466\pi\)
\(308\) 0 0
\(309\) −0.460109 2.60941i −0.0261747 0.148444i
\(310\) 0 0
\(311\) 4.22506 7.31802i 0.239581 0.414967i −0.721013 0.692922i \(-0.756323\pi\)
0.960594 + 0.277955i \(0.0896565\pi\)
\(312\) 0 0
\(313\) 1.13129 + 0.949265i 0.0639443 + 0.0536556i 0.674200 0.738549i \(-0.264489\pi\)
−0.610255 + 0.792205i \(0.708933\pi\)
\(314\) 0 0
\(315\) 4.31741 + 7.47797i 0.243258 + 0.421336i
\(316\) 0 0
\(317\) −2.10586 + 0.766472i −0.118277 + 0.0430494i −0.400481 0.916305i \(-0.631157\pi\)
0.282204 + 0.959355i \(0.408935\pi\)
\(318\) 0 0
\(319\) −5.23393 + 29.6831i −0.293044 + 1.66193i
\(320\) 0 0
\(321\) 24.0959 20.2189i 1.34490 1.12851i
\(322\) 0 0
\(323\) −1.70184 3.79260i −0.0946931 0.211026i
\(324\) 0 0
\(325\) 0.0938253 0.0787287i 0.00520449 0.00436708i
\(326\) 0 0
\(327\) 1.62484 9.21493i 0.0898539 0.509587i
\(328\) 0 0
\(329\) −1.12011 + 0.407686i −0.0617536 + 0.0224765i
\(330\) 0 0
\(331\) −1.35657 2.34964i −0.0745637 0.129148i 0.826333 0.563182i \(-0.190423\pi\)
−0.900896 + 0.434034i \(0.857090\pi\)
\(332\) 0 0
\(333\) −46.0313 38.6248i −2.52250 2.11663i
\(334\) 0 0
\(335\) −7.88961 + 13.6652i −0.431056 + 0.746610i
\(336\) 0 0
\(337\) 2.01515 + 11.4285i 0.109772 + 0.622549i 0.989206 + 0.146529i \(0.0468101\pi\)
−0.879434 + 0.476020i \(0.842079\pi\)
\(338\) 0 0
\(339\) −17.7539 6.46190i −0.964261 0.350962i
\(340\) 0 0
\(341\) 26.2173 1.41975
\(342\) 0 0
\(343\) 15.8909 0.858030
\(344\) 0 0
\(345\) 8.56438 + 3.11718i 0.461091 + 0.167823i
\(346\) 0 0
\(347\) −5.33836 30.2754i −0.286578 1.62527i −0.699593 0.714542i \(-0.746635\pi\)
0.413014 0.910725i \(-0.364476\pi\)
\(348\) 0 0
\(349\) 9.56699 16.5705i 0.512109 0.886999i −0.487792 0.872960i \(-0.662198\pi\)
0.999901 0.0140393i \(-0.00446900\pi\)
\(350\) 0 0
\(351\) −1.08348 0.909151i −0.0578321 0.0485269i
\(352\) 0 0
\(353\) −9.74328 16.8759i −0.518583 0.898211i −0.999767 0.0215918i \(-0.993127\pi\)
0.481184 0.876619i \(-0.340207\pi\)
\(354\) 0 0
\(355\) 14.1858 5.16320i 0.752902 0.274034i
\(356\) 0 0
\(357\) −0.664283 + 3.76734i −0.0351576 + 0.199389i
\(358\) 0 0
\(359\) −25.7000 + 21.5649i −1.35639 + 1.13815i −0.379317 + 0.925267i \(0.623841\pi\)
−0.977078 + 0.212884i \(0.931714\pi\)
\(360\) 0 0
\(361\) −16.1714 9.97434i −0.851124 0.524965i
\(362\) 0 0
\(363\) −22.1142 + 18.5560i −1.16069 + 0.973938i
\(364\) 0 0
\(365\) −0.667571 + 3.78598i −0.0349422 + 0.198167i
\(366\) 0 0
\(367\) −10.1767 + 3.70401i −0.531219 + 0.193348i −0.593683 0.804699i \(-0.702327\pi\)
0.0624636 + 0.998047i \(0.480104\pi\)
\(368\) 0 0
\(369\) 26.6184 + 46.1044i 1.38570 + 2.40010i
\(370\) 0 0
\(371\) 0.0235231 + 0.0197382i 0.00122126 + 0.00102476i
\(372\) 0 0
\(373\) −4.14975 + 7.18758i −0.214866 + 0.372159i −0.953231 0.302242i \(-0.902265\pi\)
0.738365 + 0.674401i \(0.235598\pi\)
\(374\) 0 0
\(375\) −0.541007 3.06820i −0.0279375 0.158441i
\(376\) 0 0
\(377\) 0.770597 + 0.280474i 0.0396878 + 0.0144452i
\(378\) 0 0
\(379\) 2.75557 0.141544 0.0707720 0.997493i \(-0.477454\pi\)
0.0707720 + 0.997493i \(0.477454\pi\)
\(380\) 0 0
\(381\) −20.6940 −1.06018
\(382\) 0 0
\(383\) 2.15130 + 0.783010i 0.109926 + 0.0400100i 0.396398 0.918079i \(-0.370260\pi\)
−0.286471 + 0.958089i \(0.592482\pi\)
\(384\) 0 0
\(385\) −1.00648 5.70805i −0.0512951 0.290909i
\(386\) 0 0
\(387\) 31.9631 55.3618i 1.62478 2.81420i
\(388\) 0 0
\(389\) −8.46044 7.09915i −0.428961 0.359941i 0.402598 0.915377i \(-0.368107\pi\)
−0.831560 + 0.555436i \(0.812552\pi\)
\(390\) 0 0
\(391\) 1.39490 + 2.41604i 0.0705433 + 0.122185i
\(392\) 0 0
\(393\) 27.0146 9.83252i 1.36271 0.495985i
\(394\) 0 0
\(395\) 0.517719 2.93613i 0.0260493 0.147733i
\(396\) 0 0
\(397\) −14.4339 + 12.1114i −0.724415 + 0.607856i −0.928603 0.371076i \(-0.878989\pi\)
0.204188 + 0.978932i \(0.434545\pi\)
\(398\) 0 0
\(399\) 7.15829 + 15.9525i 0.358363 + 0.798621i
\(400\) 0 0
\(401\) 1.34821 1.13128i 0.0673263 0.0564935i −0.608503 0.793551i \(-0.708230\pi\)
0.675830 + 0.737058i \(0.263785\pi\)
\(402\) 0 0
\(403\) 0.123863 0.702462i 0.00617005 0.0349921i
\(404\) 0 0
\(405\) −14.9018 + 5.42382i −0.740478 + 0.269512i
\(406\) 0 0
\(407\) 20.1675 + 34.9311i 0.999665 + 1.73147i
\(408\) 0 0
\(409\) −9.30115 7.80459i −0.459912 0.385912i 0.383187 0.923671i \(-0.374827\pi\)
−0.843099 + 0.537759i \(0.819271\pi\)
\(410\) 0 0
\(411\) −5.68992 + 9.85523i −0.280663 + 0.486123i
\(412\) 0 0
\(413\) −2.39224 13.5671i −0.117715 0.667593i
\(414\) 0 0
\(415\) −8.20267 2.98553i −0.402653 0.146554i
\(416\) 0 0
\(417\) 58.6508 2.87214
\(418\) 0 0
\(419\) −16.4679 −0.804509 −0.402255 0.915528i \(-0.631773\pi\)
−0.402255 + 0.915528i \(0.631773\pi\)
\(420\) 0 0
\(421\) 0.999150 + 0.363661i 0.0486956 + 0.0177237i 0.366253 0.930515i \(-0.380640\pi\)
−0.317558 + 0.948239i \(0.602863\pi\)
\(422\) 0 0
\(423\) −1.07818 6.11465i −0.0524228 0.297304i
\(424\) 0 0
\(425\) 0.476833 0.825899i 0.0231298 0.0400620i
\(426\) 0 0
\(427\) −5.82134 4.88469i −0.281715 0.236387i
\(428\) 0 0
\(429\) 0.858916 + 1.48769i 0.0414688 + 0.0718261i
\(430\) 0 0
\(431\) 32.7978 11.9374i 1.57982 0.575006i 0.604651 0.796490i \(-0.293312\pi\)
0.975164 + 0.221484i \(0.0710902\pi\)
\(432\) 0 0
\(433\) −1.23492 + 7.00358i −0.0593465 + 0.336571i −0.999996 0.00280872i \(-0.999106\pi\)
0.940650 + 0.339379i \(0.110217\pi\)
\(434\) 0 0
\(435\) 15.9795 13.4084i 0.766156 0.642882i
\(436\) 0 0
\(437\) 11.4770 + 5.55636i 0.549021 + 0.265797i
\(438\) 0 0
\(439\) −5.83392 + 4.89524i −0.278438 + 0.233637i −0.771302 0.636469i \(-0.780394\pi\)
0.492864 + 0.870106i \(0.335950\pi\)
\(440\) 0 0
\(441\) −6.22153 + 35.2841i −0.296263 + 1.68019i
\(442\) 0 0
\(443\) −16.2738 + 5.92317i −0.773191 + 0.281419i −0.698330 0.715776i \(-0.746073\pi\)
−0.0748605 + 0.997194i \(0.523851\pi\)
\(444\) 0 0
\(445\) −7.48203 12.9592i −0.354682 0.614327i
\(446\) 0 0
\(447\) −28.1080 23.5854i −1.32946 1.11555i
\(448\) 0 0
\(449\) 0.462444 0.800976i 0.0218241 0.0378004i −0.854907 0.518781i \(-0.826386\pi\)
0.876731 + 0.480981i \(0.159719\pi\)
\(450\) 0 0
\(451\) −6.20533 35.1922i −0.292197 1.65713i
\(452\) 0 0
\(453\) 20.3187 + 7.39540i 0.954656 + 0.347466i
\(454\) 0 0
\(455\) −0.157696 −0.00739289
\(456\) 0 0
\(457\) −20.6874 −0.967718 −0.483859 0.875146i \(-0.660765\pi\)
−0.483859 + 0.875146i \(0.660765\pi\)
\(458\) 0 0
\(459\) −10.3487 3.76661i −0.483035 0.175810i
\(460\) 0 0
\(461\) 2.46202 + 13.9628i 0.114667 + 0.650312i 0.986914 + 0.161246i \(0.0515512\pi\)
−0.872247 + 0.489066i \(0.837338\pi\)
\(462\) 0 0
\(463\) 18.7765 32.5218i 0.872616 1.51141i 0.0133346 0.999911i \(-0.495755\pi\)
0.859281 0.511504i \(-0.170911\pi\)
\(464\) 0 0
\(465\) −13.8993 11.6629i −0.644563 0.540852i
\(466\) 0 0
\(467\) 2.95532 + 5.11877i 0.136756 + 0.236868i 0.926267 0.376868i \(-0.122999\pi\)
−0.789511 + 0.613736i \(0.789666\pi\)
\(468\) 0 0
\(469\) 19.0909 6.94850i 0.881534 0.320852i
\(470\) 0 0
\(471\) −9.44497 + 53.5651i −0.435201 + 2.46815i
\(472\) 0 0
\(473\) −32.8713 + 27.5823i −1.51142 + 1.26823i
\(474\) 0 0
\(475\) −0.316738 4.34738i −0.0145329 0.199471i
\(476\) 0 0
\(477\) −0.122529 + 0.102814i −0.00561023 + 0.00470755i
\(478\) 0 0
\(479\) 1.61205 9.14240i 0.0736565 0.417727i −0.925576 0.378561i \(-0.876419\pi\)
0.999233 0.0391656i \(-0.0124700\pi\)
\(480\) 0 0
\(481\) 1.03122 0.375333i 0.0470196 0.0171137i
\(482\) 0 0
\(483\) −5.86724 10.1624i −0.266969 0.462403i
\(484\) 0 0
\(485\) −13.3023 11.1620i −0.604026 0.506838i
\(486\) 0 0
\(487\) 12.4983 21.6477i 0.566353 0.980951i −0.430570 0.902557i \(-0.641687\pi\)
0.996922 0.0783942i \(-0.0249793\pi\)
\(488\) 0 0
\(489\) 6.62847 + 37.5919i 0.299750 + 1.69997i
\(490\) 0 0
\(491\) −21.1513 7.69846i −0.954547 0.347427i −0.182652 0.983178i \(-0.558468\pi\)
−0.771894 + 0.635751i \(0.780691\pi\)
\(492\) 0 0
\(493\) 6.38516 0.287573
\(494\) 0 0
\(495\) 30.1913 1.35700
\(496\) 0 0
\(497\) −18.2645 6.64772i −0.819273 0.298191i
\(498\) 0 0
\(499\) −4.60596 26.1217i −0.206191 1.16937i −0.895555 0.444951i \(-0.853221\pi\)
0.689364 0.724415i \(-0.257890\pi\)
\(500\) 0 0
\(501\) −36.7480 + 63.6494i −1.64178 + 2.84364i
\(502\) 0 0
\(503\) −30.1792 25.3234i −1.34563 1.12911i −0.980142 0.198296i \(-0.936459\pi\)
−0.365484 0.930818i \(-0.619096\pi\)
\(504\) 0 0
\(505\) 3.63352 + 6.29345i 0.161690 + 0.280055i
\(506\) 0 0
\(507\) −38.0155 + 13.8365i −1.68833 + 0.614500i
\(508\) 0 0
\(509\) −3.40757 + 19.3253i −0.151038 + 0.856578i 0.811281 + 0.584656i \(0.198771\pi\)
−0.962319 + 0.271922i \(0.912341\pi\)
\(510\) 0 0
\(511\) 3.79171 3.18162i 0.167735 0.140747i
\(512\) 0 0
\(513\) −48.8052 + 12.3198i −2.15480 + 0.543930i
\(514\) 0 0
\(515\) 0.651497 0.546671i 0.0287084 0.0240892i
\(516\) 0 0
\(517\) −0.723724 + 4.10444i −0.0318294 + 0.180513i
\(518\) 0 0
\(519\) −30.5117 + 11.1053i −1.33931 + 0.487470i
\(520\) 0 0
\(521\) −8.49964 14.7218i −0.372376 0.644974i 0.617554 0.786528i \(-0.288124\pi\)
−0.989931 + 0.141554i \(0.954790\pi\)
\(522\) 0 0
\(523\) 25.3000 + 21.2293i 1.10629 + 0.928291i 0.997832 0.0658102i \(-0.0209632\pi\)
0.108461 + 0.994101i \(0.465408\pi\)
\(524\) 0 0
\(525\) −2.00566 + 3.47390i −0.0875340 + 0.151613i
\(526\) 0 0
\(527\) −0.964433 5.46957i −0.0420114 0.238258i
\(528\) 0 0
\(529\) 13.5714 + 4.93957i 0.590059 + 0.214764i
\(530\) 0 0
\(531\) 71.7597 3.11410
\(532\) 0 0
\(533\) −0.972250 −0.0421128
\(534\) 0 0
\(535\) 9.48731 + 3.45310i 0.410172 + 0.149290i
\(536\) 0 0
\(537\) −4.54675 25.7859i −0.196207 1.11274i
\(538\) 0 0
\(539\) 12.0249 20.8277i 0.517947 0.897111i
\(540\) 0 0
\(541\) −15.8252 13.2789i −0.680378 0.570905i 0.235739 0.971816i \(-0.424249\pi\)
−0.916117 + 0.400912i \(0.868693\pi\)
\(542\) 0 0
\(543\) 35.1086 + 60.8099i 1.50666 + 2.60960i
\(544\) 0 0
\(545\) 2.82224 1.02721i 0.120891 0.0440009i
\(546\) 0 0
\(547\) 3.19901 18.1425i 0.136780 0.775717i −0.836824 0.547472i \(-0.815590\pi\)
0.973604 0.228245i \(-0.0732988\pi\)
\(548\) 0 0
\(549\) 30.3228 25.4438i 1.29414 1.08592i
\(550\) 0 0
\(551\) 24.1474 16.3902i 1.02871 0.698248i
\(552\) 0 0
\(553\) −2.94057 + 2.46743i −0.125046 + 0.104926i
\(554\) 0 0
\(555\) 4.84733 27.4906i 0.205758 1.16691i
\(556\) 0 0
\(557\) 30.4882 11.0968i 1.29183 0.470186i 0.397500 0.917602i \(-0.369878\pi\)
0.894326 + 0.447416i \(0.147656\pi\)
\(558\) 0 0
\(559\) 0.583735 + 1.01106i 0.0246894 + 0.0427632i
\(560\) 0 0
\(561\) 10.2463 + 8.59763i 0.432597 + 0.362992i
\(562\) 0 0
\(563\) −4.29185 + 7.43371i −0.180880 + 0.313293i −0.942180 0.335106i \(-0.891228\pi\)
0.761300 + 0.648399i \(0.224561\pi\)
\(564\) 0 0
\(565\) −1.05304 5.97211i −0.0443019 0.251248i
\(566\) 0 0
\(567\) 19.1864 + 6.98328i 0.805753 + 0.293270i
\(568\) 0 0
\(569\) 18.8173 0.788861 0.394431 0.918926i \(-0.370942\pi\)
0.394431 + 0.918926i \(0.370942\pi\)
\(570\) 0 0
\(571\) −9.57993 −0.400907 −0.200454 0.979703i \(-0.564242\pi\)
−0.200454 + 0.979703i \(0.564242\pi\)
\(572\) 0 0
\(573\) 71.1322 + 25.8900i 2.97159 + 1.08157i
\(574\) 0 0
\(575\) 0.507981 + 2.88091i 0.0211843 + 0.120142i
\(576\) 0 0
\(577\) 6.41220 11.1063i 0.266943 0.462359i −0.701128 0.713036i \(-0.747320\pi\)
0.968071 + 0.250676i \(0.0806530\pi\)
\(578\) 0 0
\(579\) 11.0880 + 9.30396i 0.460803 + 0.386660i
\(580\) 0 0
\(581\) 5.61944 + 9.73316i 0.233134 + 0.403799i
\(582\) 0 0
\(583\) 0.100892 0.0367215i 0.00417850 0.00152085i
\(584\) 0 0
\(585\) 0.142638 0.808941i 0.00589736 0.0334456i
\(586\) 0 0
\(587\) −20.7329 + 17.3970i −0.855739 + 0.718050i −0.961046 0.276390i \(-0.910862\pi\)
0.105307 + 0.994440i \(0.466417\pi\)
\(588\) 0 0
\(589\) −17.6873 18.2092i −0.728791 0.750295i
\(590\) 0 0
\(591\) 28.6569 24.0460i 1.17879 0.989120i
\(592\) 0 0
\(593\) −5.90373 + 33.4817i −0.242437 + 1.37493i 0.583933 + 0.811802i \(0.301513\pi\)
−0.826370 + 0.563127i \(0.809598\pi\)
\(594\) 0 0
\(595\) −1.15382 + 0.419954i −0.0473018 + 0.0172164i
\(596\) 0 0
\(597\) 18.2205 + 31.5588i 0.745714 + 1.29161i
\(598\) 0 0
\(599\) 0.383051 + 0.321418i 0.0156510 + 0.0131328i 0.650580 0.759438i \(-0.274526\pi\)
−0.634929 + 0.772571i \(0.718970\pi\)
\(600\) 0 0
\(601\) −3.43562 + 5.95066i −0.140142 + 0.242733i −0.927550 0.373699i \(-0.878089\pi\)
0.787408 + 0.616432i \(0.211422\pi\)
\(602\) 0 0
\(603\) 18.3762 + 104.217i 0.748336 + 4.24402i
\(604\) 0 0
\(605\) −8.70704 3.16910i −0.353991 0.128842i
\(606\) 0 0
\(607\) −7.65201 −0.310586 −0.155293 0.987868i \(-0.549632\pi\)
−0.155293 + 0.987868i \(0.549632\pi\)
\(608\) 0 0
\(609\) −26.8573 −1.08831
\(610\) 0 0
\(611\) 0.106555 + 0.0387827i 0.00431074 + 0.00156898i
\(612\) 0 0
\(613\) −5.77627 32.7589i −0.233302 1.32312i −0.846161 0.532927i \(-0.821092\pi\)
0.612860 0.790192i \(-0.290019\pi\)
\(614\) 0 0
\(615\) −12.3656 + 21.4178i −0.498629 + 0.863650i
\(616\) 0 0
\(617\) 11.5490 + 9.69076i 0.464945 + 0.390135i 0.844947 0.534851i \(-0.179632\pi\)
−0.380002 + 0.924986i \(0.624077\pi\)
\(618\) 0 0
\(619\) −15.4112 26.6930i −0.619428 1.07288i −0.989590 0.143914i \(-0.954031\pi\)
0.370162 0.928967i \(-0.379302\pi\)
\(620\) 0 0
\(621\) 31.7443 11.5540i 1.27386 0.463645i
\(622\) 0 0
\(623\) −3.34560 + 18.9738i −0.134038 + 0.760170i
\(624\) 0 0
\(625\) 0.766044 0.642788i 0.0306418 0.0257115i
\(626\) 0 0
\(627\) 60.8187 + 6.21308i 2.42887 + 0.248126i
\(628\) 0 0
\(629\) 6.54561 5.49242i 0.260990 0.218997i
\(630\) 0 0
\(631\) −5.76052 + 32.6695i −0.229323 + 1.30055i 0.624924 + 0.780685i \(0.285130\pi\)
−0.854247 + 0.519868i \(0.825981\pi\)
\(632\) 0 0
\(633\) 36.8297 13.4049i 1.46385 0.532798i
\(634\) 0 0
\(635\) −3.32109 5.75230i −0.131794 0.228273i
\(636\) 0 0
\(637\) −0.501242 0.420592i −0.0198599 0.0166645i
\(638\) 0 0
\(639\) 50.6217 87.6793i 2.00256 3.46854i
\(640\) 0 0
\(641\) −3.69073 20.9312i −0.145775 0.826732i −0.966741 0.255756i \(-0.917676\pi\)
0.820966 0.570977i \(-0.193435\pi\)
\(642\) 0 0
\(643\) −43.7776 15.9338i −1.72642 0.628366i −0.728056 0.685517i \(-0.759576\pi\)
−0.998366 + 0.0571513i \(0.981798\pi\)
\(644\) 0 0
\(645\) 29.6970 1.16932
\(646\) 0 0
\(647\) 4.02896 0.158395 0.0791974 0.996859i \(-0.474764\pi\)
0.0791974 + 0.996859i \(0.474764\pi\)
\(648\) 0 0
\(649\) −45.2636 16.4746i −1.77675 0.646685i
\(650\) 0 0
\(651\) 4.05660 + 23.0061i 0.158991 + 0.901681i
\(652\) 0 0
\(653\) −6.38069 + 11.0517i −0.249696 + 0.432486i −0.963441 0.267919i \(-0.913664\pi\)
0.713746 + 0.700405i \(0.246997\pi\)
\(654\) 0 0
\(655\) 7.06862 + 5.93127i 0.276194 + 0.231754i
\(656\) 0 0
\(657\) 12.8913 + 22.3284i 0.502937 + 0.871112i
\(658\) 0 0
\(659\) 17.6911 6.43902i 0.689146 0.250829i 0.0263766 0.999652i \(-0.491603\pi\)
0.662770 + 0.748823i \(0.269381\pi\)
\(660\) 0 0
\(661\) 2.07438 11.7644i 0.0806842 0.457583i −0.917521 0.397688i \(-0.869812\pi\)
0.998205 0.0598944i \(-0.0190764\pi\)
\(662\) 0 0
\(663\) 0.278772 0.233917i 0.0108266 0.00908459i
\(664\) 0 0
\(665\) −3.28550 + 4.54994i −0.127406 + 0.176439i
\(666\) 0 0
\(667\) −15.0040 + 12.5899i −0.580957 + 0.487481i
\(668\) 0 0
\(669\) −7.29544 + 41.3745i −0.282058 + 1.59963i
\(670\) 0 0
\(671\) −24.9680 + 9.08760i −0.963878 + 0.350823i
\(672\) 0 0
\(673\) 11.9605 + 20.7161i 0.461042 + 0.798547i 0.999013 0.0444155i \(-0.0141426\pi\)
−0.537972 + 0.842963i \(0.680809\pi\)
\(674\) 0 0
\(675\) −8.84620 7.42284i −0.340490 0.285705i
\(676\) 0 0
\(677\) −5.45024 + 9.44010i −0.209470 + 0.362812i −0.951548 0.307501i \(-0.900507\pi\)
0.742078 + 0.670314i \(0.233840\pi\)
\(678\) 0 0
\(679\) 3.88237 + 22.0180i 0.148992 + 0.844973i
\(680\) 0 0
\(681\) −61.7996 22.4932i −2.36816 0.861941i
\(682\) 0 0
\(683\) −0.353548 −0.0135282 −0.00676408 0.999977i \(-0.502153\pi\)
−0.00676408 + 0.999977i \(0.502153\pi\)
\(684\) 0 0
\(685\) −3.65261 −0.139559
\(686\) 0 0
\(687\) −56.6878 20.6327i −2.16278 0.787186i
\(688\) 0 0
\(689\) −0.000507251 0.00287676i −1.93247e−5 0.000109596i
\(690\) 0 0
\(691\) −1.06320 + 1.84152i −0.0404460 + 0.0700546i −0.885540 0.464564i \(-0.846211\pi\)
0.845094 + 0.534618i \(0.179545\pi\)
\(692\) 0 0
\(693\) −29.7776 24.9864i −1.13116 0.949153i
\(694\) 0 0
\(695\) 9.41264 + 16.3032i 0.357042 + 0.618415i
\(696\) 0 0
\(697\) −7.11368 + 2.58917i −0.269450 + 0.0980718i
\(698\) 0 0
\(699\) 1.00202 5.68274i 0.0378999 0.214941i
\(700\) 0 0
\(701\) 16.4345 13.7902i 0.620722 0.520848i −0.277308 0.960781i \(-0.589442\pi\)
0.898030 + 0.439933i \(0.144998\pi\)
\(702\) 0 0
\(703\) 10.6555 37.5733i 0.401880 1.41710i
\(704\) 0 0
\(705\) 2.20957 1.85405i 0.0832171 0.0698274i
\(706\) 0 0
\(707\) 1.62473 9.21432i 0.0611044 0.346540i
\(708\) 0 0
\(709\) 39.1314 14.2427i 1.46961 0.534895i 0.521616 0.853180i \(-0.325329\pi\)
0.947995 + 0.318286i \(0.103107\pi\)
\(710\) 0 0
\(711\) −9.99754 17.3162i −0.374937 0.649410i
\(712\) 0 0
\(713\) 13.0508 + 10.9509i 0.488756 + 0.410115i
\(714\) 0 0
\(715\) −0.275688 + 0.477506i −0.0103102 + 0.0178577i
\(716\) 0 0
\(717\) 11.5542 + 65.5272i 0.431500 + 2.44716i
\(718\) 0 0
\(719\) 11.1111 + 4.04411i 0.414374 + 0.150820i 0.540790 0.841157i \(-0.318125\pi\)
−0.126416 + 0.991977i \(0.540347\pi\)
\(720\) 0 0
\(721\) −1.09499 −0.0407797
\(722\) 0 0
\(723\) 18.8297 0.700285
\(724\) 0 0
\(725\) 6.29160 + 2.28996i 0.233664 + 0.0850469i
\(726\) 0 0
\(727\) 1.05821 + 6.00138i 0.0392467 + 0.222579i 0.998123 0.0612463i \(-0.0195075\pi\)
−0.958876 + 0.283825i \(0.908396\pi\)
\(728\) 0 0
\(729\) 0.789882 1.36812i 0.0292549 0.0506709i
\(730\) 0 0
\(731\) 6.96355 + 5.84311i 0.257556 + 0.216115i
\(732\) 0 0
\(733\) −26.7539 46.3391i −0.988177 1.71157i −0.626867 0.779126i \(-0.715663\pi\)
−0.361310 0.932446i \(-0.617670\pi\)
\(734\) 0 0
\(735\) −15.6403 + 5.69262i −0.576902 + 0.209975i
\(736\) 0 0
\(737\) 12.3350 69.9551i 0.454365 2.57683i
\(738\) 0 0
\(739\) 22.9031 19.2180i 0.842504 0.706945i −0.115621 0.993293i \(-0.536886\pi\)
0.958126 + 0.286348i \(0.0924415\pi\)
\(740\) 0 0
\(741\) 0.453809 1.60021i 0.0166711 0.0587853i
\(742\) 0 0
\(743\) −36.6959 + 30.7915i −1.34624 + 1.12963i −0.366268 + 0.930510i \(0.619365\pi\)
−0.979975 + 0.199122i \(0.936191\pi\)
\(744\) 0 0
\(745\) 2.04509 11.5983i 0.0749264 0.424929i
\(746\) 0 0
\(747\) −55.0116 + 20.0226i −2.01277 + 0.732588i
\(748\) 0 0
\(749\) −6.49952 11.2575i −0.237487 0.411340i
\(750\) 0 0
\(751\) 19.4465 + 16.3175i 0.709611 + 0.595434i 0.924490 0.381206i \(-0.124491\pi\)
−0.214879 + 0.976641i \(0.568936\pi\)
\(752\) 0 0
\(753\) −3.81448 + 6.60688i −0.139008 + 0.240768i
\(754\) 0 0
\(755\) 1.20517 + 6.83485i 0.0438606 + 0.248746i
\(756\) 0 0
\(757\) −24.9241 9.07161i −0.905880 0.329713i −0.153274 0.988184i \(-0.548982\pi\)
−0.752607 + 0.658470i \(0.771204\pi\)
\(758\) 0 0
\(759\) −41.0291 −1.48926
\(760\) 0 0
\(761\) 42.9695 1.55764 0.778822 0.627244i \(-0.215817\pi\)
0.778822 + 0.627244i \(0.215817\pi\)
\(762\) 0 0
\(763\) −3.63369 1.32255i −0.131548 0.0478797i
\(764\) 0 0
\(765\) −1.11062 6.29865i −0.0401546 0.227728i
\(766\) 0 0
\(767\) −0.655265 + 1.13495i −0.0236602 + 0.0409807i
\(768\) 0 0
\(769\) −36.0908 30.2838i −1.30147 1.09206i −0.989890 0.141839i \(-0.954698\pi\)
−0.311577 0.950221i \(-0.600857\pi\)
\(770\) 0 0
\(771\) 15.7776 + 27.3277i 0.568217 + 0.984182i
\(772\) 0 0
\(773\) −20.4768 + 7.45294i −0.736499 + 0.268064i −0.682913 0.730499i \(-0.739287\pi\)
−0.0535859 + 0.998563i \(0.517065\pi\)
\(774\) 0 0
\(775\) 1.01129 5.73531i 0.0363266 0.206018i
\(776\) 0 0
\(777\) −27.5321 + 23.1022i −0.987710 + 0.828787i
\(778\) 0 0
\(779\) −20.2563 + 28.0520i −0.725756 + 1.00507i
\(780\) 0 0
\(781\) −52.0599 + 43.6834i −1.86285 + 1.56312i
\(782\) 0 0
\(783\) 13.4261 76.1430i 0.479808 2.72113i
\(784\) 0 0
\(785\) −16.4053 + 5.97103i −0.585530 + 0.213115i
\(786\) 0 0
\(787\) −24.0963 41.7360i −0.858940 1.48773i −0.872941 0.487826i \(-0.837790\pi\)
0.0140010 0.999902i \(-0.495543\pi\)
\(788\) 0 0
\(789\) −26.3254 22.0896i −0.937210 0.786412i
\(790\) 0 0
\(791\) −3.90391 + 6.76177i −0.138807 + 0.240421i
\(792\) 0 0
\(793\) 0.125531 + 0.711922i 0.00445774 + 0.0252811i
\(794\) 0 0
\(795\) −0.0698241 0.0254139i −0.00247640 0.000901338i
\(796\) 0 0
\(797\) 22.8798 0.810443 0.405221 0.914219i \(-0.367194\pi\)
0.405221 + 0.914219i \(0.367194\pi\)
\(798\) 0 0
\(799\) 0.882911 0.0312352
\(800\) 0 0
\(801\) −94.3049 34.3242i −3.33210 1.21279i
\(802\) 0 0
\(803\) −3.00524 17.0436i −0.106053 0.601455i
\(804\) 0 0
\(805\) 1.88322 3.26184i 0.0663748 0.114965i
\(806\) 0 0
\(807\) 47.6385 + 39.9735i 1.67696 + 1.40713i
\(808\) 0 0
\(809\) −5.54829 9.60992i −0.195068 0.337867i 0.751855 0.659328i \(-0.229159\pi\)
−0.946923 + 0.321461i \(0.895826\pi\)
\(810\) 0 0
\(811\) 4.68468 1.70509i 0.164502 0.0598737i −0.258457 0.966023i \(-0.583214\pi\)
0.422958 + 0.906149i \(0.360992\pi\)
\(812\) 0 0
\(813\) 3.07914 17.4627i 0.107990 0.612443i
\(814\) 0 0
\(815\) −9.38566 + 7.87550i −0.328765 + 0.275867i
\(816\) 0 0
\(817\) 41.3335 + 4.22252i 1.44608 + 0.147727i
\(818\) 0 0
\(819\) −0.810164 + 0.679808i −0.0283094 + 0.0237544i
\(820\) 0 0
\(821\) −4.09160 + 23.2046i −0.142798 + 0.809847i 0.826311 + 0.563214i \(0.190435\pi\)
−0.969109 + 0.246633i \(0.920676\pi\)
\(822\) 0 0
\(823\) 41.1290 14.9697i 1.43367 0.521812i 0.495687 0.868501i \(-0.334916\pi\)
0.937980 + 0.346689i \(0.112694\pi\)
\(824\) 0 0
\(825\) 7.01269 + 12.1463i 0.244151 + 0.422881i
\(826\) 0 0
\(827\) −6.73462 5.65102i −0.234186 0.196505i 0.518141 0.855295i \(-0.326624\pi\)
−0.752327 + 0.658790i \(0.771069\pi\)
\(828\) 0 0
\(829\) −16.3329 + 28.2894i −0.567264 + 0.982530i 0.429571 + 0.903033i \(0.358665\pi\)
−0.996835 + 0.0794970i \(0.974669\pi\)
\(830\) 0 0
\(831\) −17.4046 98.7064i −0.603759 3.42409i
\(832\) 0 0
\(833\) −4.78751 1.74251i −0.165877 0.0603745i
\(834\) 0 0
\(835\) −23.5902 −0.816372
\(836\) 0 0
\(837\) −67.2524 −2.32458
\(838\) 0 0
\(839\) 18.5786 + 6.76204i 0.641403 + 0.233452i 0.642187 0.766548i \(-0.278027\pi\)
−0.000783927 1.00000i \(0.500250\pi\)
\(840\) 0 0
\(841\) 2.74854 + 15.5877i 0.0947771 + 0.537508i
\(842\) 0 0
\(843\) 20.9688 36.3190i 0.722204 1.25089i
\(844\) 0 0
\(845\) −9.94709 8.34660i −0.342190 0.287132i
\(846\) 0 0
\(847\) 5.96498 + 10.3316i 0.204959 + 0.354999i
\(848\) 0 0
\(849\) 22.0490 8.02519i 0.756721 0.275424i
\(850\) 0 0
\(851\) −4.55142 + 25.8124i −0.156021 + 0.884838i
\(852\) 0 0
\(853\) 26.0634 21.8698i 0.892394 0.748808i −0.0762946 0.997085i \(-0.524309\pi\)
0.968689 + 0.248278i \(0.0798645\pi\)
\(854\) 0 0
\(855\) −20.3683 20.9693i −0.696581 0.717135i
\(856\) 0 0
\(857\) 12.9066 10.8299i 0.440881 0.369943i −0.395158 0.918613i \(-0.629310\pi\)
0.836039 + 0.548670i \(0.184866\pi\)
\(858\) 0 0
\(859\) −0.729186 + 4.13542i −0.0248795 + 0.141099i −0.994717 0.102653i \(-0.967267\pi\)
0.969838 + 0.243751i \(0.0783781\pi\)
\(860\) 0 0
\(861\) 29.9216 10.8906i 1.01972 0.371149i
\(862\) 0 0
\(863\) −18.5050 32.0517i −0.629919 1.09105i −0.987568 0.157195i \(-0.949755\pi\)
0.357649 0.933856i \(-0.383579\pi\)
\(864\) 0 0
\(865\) −7.98365 6.69908i −0.271452 0.227775i
\(866\) 0 0
\(867\) −25.0653 + 43.4143i −0.851262 + 1.47443i
\(868\) 0 0
\(869\) 2.33065 + 13.2178i 0.0790618 + 0.448382i
\(870\) 0 0
\(871\) −1.81609 0.661003i −0.0615359 0.0223972i
\(872\) 0 0
\(873\) −116.459 −3.94153
\(874\) 0 0
\(875\) −1.28752 −0.0435261
\(876\) 0 0
\(877\) 28.6083 + 10.4126i 0.966032 + 0.351607i 0.776395 0.630247i \(-0.217046\pi\)
0.189638 + 0.981854i \(0.439269\pi\)
\(878\) 0 0
\(879\) 13.4078 + 76.0392i 0.452233 + 2.56474i
\(880\) 0 0
\(881\) 5.10993 8.85066i 0.172158 0.298186i −0.767016 0.641628i \(-0.778259\pi\)
0.939174 + 0.343442i \(0.111593\pi\)
\(882\) 0 0
\(883\) −20.8764 17.5174i −0.702548 0.589508i 0.219949 0.975511i \(-0.429411\pi\)
−0.922497 + 0.386003i \(0.873855\pi\)
\(884\) 0 0
\(885\) 16.6680 + 28.8698i 0.560289 + 0.970449i
\(886\) 0 0
\(887\) −46.7138 + 17.0024i −1.56849 + 0.570885i −0.972662 0.232223i \(-0.925400\pi\)
−0.595832 + 0.803109i \(0.703178\pi\)
\(888\) 0 0
\(889\) −1.48503 + 8.42202i −0.0498063 + 0.282466i
\(890\) 0 0
\(891\) 54.6877 45.8884i 1.83211 1.53732i
\(892\) 0 0
\(893\) 3.33899 2.26637i 0.111735 0.0758411i
\(894\) 0 0
\(895\) 6.43803 5.40215i 0.215199 0.180574i
\(896\) 0 0
\(897\) −0.193841 + 1.09933i −0.00647217 + 0.0367055i
\(898\) 0 0
\(899\) 36.6410 13.3362i 1.22204 0.444788i
\(900\) 0 0
\(901\) −0.0113724 0.0196976i −0.000378871 0.000656223i
\(902\) 0 0
\(903\) −29.2901 24.5773i −0.974713 0.817881i
\(904\) 0 0
\(905\) −11.2689 + 19.5183i −0.374591 + 0.648810i
\(906\) 0 0
\(907\) −3.81396 21.6301i −0.126641 0.718215i −0.980320 0.197416i \(-0.936745\pi\)
0.853679 0.520799i \(-0.174366\pi\)
\(908\) 0 0
\(909\) 45.7977 + 16.6690i 1.51901 + 0.552875i
\(910\) 0 0
\(911\) −6.97667 −0.231148 −0.115574 0.993299i \(-0.536871\pi\)
−0.115574 + 0.993299i \(0.536871\pi\)
\(912\) 0 0
\(913\) 39.2963 1.30052
\(914\) 0 0
\(915\) 17.2796 + 6.28926i 0.571246 + 0.207917i
\(916\) 0 0
\(917\) −2.06303 11.7000i −0.0681271 0.386368i
\(918\) 0 0
\(919\) −0.179981 + 0.311736i −0.00593702 + 0.0102832i −0.868979 0.494850i \(-0.835223\pi\)
0.863042 + 0.505133i \(0.168556\pi\)
\(920\) 0 0
\(921\) 41.1278 + 34.5103i 1.35521 + 1.13715i
\(922\) 0 0
\(923\) 0.924491 + 1.60127i 0.0304300 + 0.0527063i
\(924\) 0 0
\(925\) 8.41948 3.06444i 0.276831 0.100758i
\(926\) 0 0
\(927\) 0.990439 5.61706i 0.0325303 0.184488i
\(928\) 0 0
\(929\) 9.16646 7.69157i 0.300742 0.252352i −0.479911 0.877317i \(-0.659331\pi\)
0.780653 + 0.624965i \(0.214887\pi\)
\(930\) 0 0
\(931\) −22.5783 + 5.69937i −0.739973 + 0.186789i
\(932\) 0 0
\(933\) 20.1674 16.9224i 0.660250 0.554016i
\(934\) 0 0
\(935\) −0.745502 + 4.22795i −0.0243805 + 0.138269i
\(936\) 0 0
\(937\) 26.8842 9.78505i 0.878269 0.319664i 0.136758 0.990604i \(-0.456332\pi\)
0.741511 + 0.670941i \(0.234110\pi\)
\(938\) 0 0
\(939\) 2.30050 + 3.98458i 0.0750740 + 0.130032i
\(940\) 0 0
\(941\) 15.4644 + 12.9762i 0.504126 + 0.423012i 0.859057 0.511881i \(-0.171051\pi\)
−0.354930 + 0.934893i \(0.615495\pi\)
\(942\) 0 0
\(943\) 11.6107 20.1104i 0.378098 0.654884i
\(944\) 0 0
\(945\) 2.58183 + 14.6423i 0.0839868 + 0.476313i
\(946\) 0 0
\(947\) 19.2743 + 7.01526i 0.626330 + 0.227965i 0.635633 0.771991i \(-0.280739\pi\)
−0.00930331 + 0.999957i \(0.502961\pi\)
\(948\) 0 0
\(949\) −0.470861 −0.0152848
\(950\) 0 0
\(951\) −6.98196 −0.226405
\(952\) 0 0
\(953\) 44.9752 + 16.3696i 1.45689 + 0.530265i 0.944507 0.328492i \(-0.106540\pi\)
0.512384 + 0.858756i \(0.328762\pi\)
\(954\) 0 0
\(955\) 4.21909 + 23.9276i 0.136526 + 0.774280i
\(956\) 0 0
\(957\) −46.9527 + 81.3244i −1.51776 + 2.62885i
\(958\) 0 0
\(959\) 3.60256 + 3.02291i 0.116333 + 0.0976148i
\(960\) 0 0
\(961\) −1.45823 2.52573i −0.0470398 0.0814752i
\(962\) 0 0
\(963\) 63.6271 23.1584i 2.05036 0.746268i
\(964\) 0 0
\(965\) −0.806749 + 4.57530i −0.0259702 + 0.147284i
\(966\) 0 0
\(967\) −9.80608 + 8.22828i −0.315342 + 0.264604i −0.786696 0.617341i \(-0.788210\pi\)
0.471354 + 0.881944i \(0.343766\pi\)
\(968\) 0 0
\(969\) −0.941086 12.9168i −0.0302320 0.414949i
\(970\) 0 0
\(971\) 21.5441 18.0776i 0.691381 0.580138i −0.227926 0.973679i \(-0.573194\pi\)
0.919307 + 0.393541i \(0.128750\pi\)
\(972\) 0 0
\(973\) 4.20887 23.8697i 0.134930 0.765227i
\(974\) 0 0
\(975\) 0.358578 0.130512i 0.0114837 0.00417972i
\(976\) 0 0
\(977\) 7.66796 + 13.2813i 0.245320 + 0.424906i 0.962221 0.272268i \(-0.0877737\pi\)
−0.716902 + 0.697174i \(0.754440\pi\)
\(978\) 0 0
\(979\) 51.6042 + 43.3011i 1.64928 + 1.38391i
\(980\) 0 0
\(981\) 10.0711 17.4437i 0.321546 0.556933i
\(982\) 0 0
\(983\) 5.27909 + 29.9392i 0.168377 + 0.954913i 0.945514 + 0.325582i \(0.105560\pi\)
−0.777137 + 0.629331i \(0.783329\pi\)
\(984\) 0 0
\(985\) 11.2831 + 4.10671i 0.359510 + 0.130851i
\(986\) 0 0
\(987\) −3.71370 −0.118208
\(988\) 0 0
\(989\) −27.8842 −0.886665
\(990\) 0 0
\(991\) −6.16155 2.24262i −0.195728 0.0712392i 0.242296 0.970202i \(-0.422099\pi\)
−0.438024 + 0.898963i \(0.644322\pi\)
\(992\) 0 0
\(993\) −1.46782 8.32445i −0.0465800 0.264168i
\(994\) 0 0
\(995\) −5.84826 + 10.1295i −0.185402 + 0.321126i
\(996\) 0 0
\(997\) −2.92015 2.45030i −0.0924821 0.0776017i 0.595374 0.803448i \(-0.297004\pi\)
−0.687856 + 0.725847i \(0.741448\pi\)
\(998\) 0 0
\(999\) −51.7335 89.6051i −1.63678 2.83498i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 380.2.u.b.101.3 18
19.4 even 9 7220.2.a.w.1.1 9
19.15 odd 18 7220.2.a.y.1.9 9
19.16 even 9 inner 380.2.u.b.301.3 yes 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
380.2.u.b.101.3 18 1.1 even 1 trivial
380.2.u.b.301.3 yes 18 19.16 even 9 inner
7220.2.a.w.1.1 9 19.4 even 9
7220.2.a.y.1.9 9 19.15 odd 18